iiinova — where your digital self keeps evolving

Philipp Wacker @phkwacker.bsky.social · 26/09/2026

Little acts of rebellion are what keep up my spirits

Textbook: "... it is easy (good exercise) to check that ...", but I crossed out the word "easy"

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Philipp Wacker @phkwacker.bsky.social · 21/08/2026

I'm sure my kids enjoyed the brief typography lecture I gave them when they asked me what went wrong here

Back of popcorn bag, text has all "fi" and "fl" missing (replaced by a square placeholder)

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Philipp Wacker @phkwacker.bsky.social · 19/05/2026

My library hold came through! Have been looking forward to reading The Edge of Space-Time by @chanda.blacksky.app for a long time!

My hand is holding a copy of "The Edge of space-time" by Dr. Chanda Prescod-Weinstein

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Philipp Wacker @phkwacker.bsky.social · 07/12/2025

I think we need another symbol for the product integral, like this:

four symbols arranged in a 2-by-2 grid (finite versus infinitesimal, and sum versus product). Showing a sum symbol (capital Sigma) for finite sum, an integral symbols for infinitesimal sum, a product symbol (capital Pi) for finite product, and a stylised, integral-font capital P (like an integral symbol with an additional arc for the "belly" of the capital P) for infinitesimal product.

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Philipp Wacker @phkwacker.bsky.social · 07/12/2025

Am I the only one who is annoyed that we don't have a special symbol for the product integral? The \Sigma becomes and \int when we take the limit in the (Riemann) integral approximation, but the \Pi just stays a \Pi when we make a product integral!

$A two-by-two panel showing (top left) a Riemann integral sum approximation \sum_{i=1}^N f(x_i)\Delta x_i, (top right, and connected with an arrow saying "limit") a definite integral \int_a^b f(x) dx. Bottom left: A finite product approximation of the product integral \sum_{i=1}^N (1 + f(x_i)\Delta x_i), connecting to bottom right with an arrow to a product integral \prod_a^b (1+f(x) dx)$

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Philipp Wacker @phkwacker.bsky.social · 02/08/2025

Relevant xkcd. imgs.xkcd.com/comics/thesi...

A woman in front of a seminar room (implied to be the PhD candidate in a defense), yelling "In conclusion, AAAAAAAA!!!" while charging towards her examiners. Subtitled: The best thesis defense is a good thesis offense

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Philipp Wacker @phkwacker.bsky.social · 29/07/2025

The last few weeks I have been using our fantastic UC makerspace (with its 3d printers, soldering iron, and tools) to print the OpenFlexure Project Manual Microscope. Kudos to @openflexure.bsky.social for an amazing open source design. Looking forward to looking at pond water and earth critters.

3d-printed microscope in black, gray, and light blue. Shows a power source consisting of 3 AA batteries and badly soldered connections.

A hair follicle under magnification. Looks like a black-ish twisted worm with four edges (?)

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Philipp Wacker @phkwacker.bsky.social · 17/07/2025

I found more!

$u(\cdot) = \cdot^{1-\rho}/(1-\rho), but they used a fancy bold version of \cdot.$ $g \equiv \Gamma^4 - 1^{57}, but 4 is a power, and 57 is a footnote marker$ crossed out "Agemo" (horse shoe). Looks like a symbol for bad luck

crossed out "Agemo" (horse shoe). Looks like a symbol for bad luck

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Philipp Wacker @phkwacker.bsky.social · 17/07/2025

Next time I run out of symbols/letters for a paper, I will take my cue from the ridiculous stuff economists seem to be get away with. This is all from a single publication.

(grave) accented beta, boldly generalising the concept of pitch accent from vowels to consonants.

A hebrew Dalet, and a strike-out capital, no-serif D. The strike out comes directly after an inline "/", leading to two diagonal lines with very different meaning. I would have given bonus points for combining Dalet with a capital Gamma but it seems the authors chickened out at the last time.

vertically flipped capital Omega ("Agemo"?), superscript g

word-final version of lower case sigma, multiplied by "normal" lower-case sigma (squared), subscript capital Xi (cursive!)

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Philipp Wacker @phkwacker.bsky.social · 03/06/2025

What is the correct metre for the "woof, woof, woof, woof" part of "Who let the dogs out"? This has been on my mind too much recently, so here's my attempt. You're welcome, internet. (or am I wrong?)

four bits of "woof", on ONE-e-and-e-two-e-AND-e-three-e-AND-e-four-E-and-e

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Philipp Wacker @phkwacker.bsky.social · 14/05/2025

the sound that you're hearing is global maths research grinding to a halt

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Philipp Wacker @phkwacker.bsky.social · 13/05/2025

New dating platform for tradies just dropped

Photo of "Pro-strength Liquid PLUMR clog destroyer gel"

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Philipp Wacker @phkwacker.bsky.social · 27/04/2025

One of the most fun things about reading comic books in languages you are trying to learn is that you learn "comic speak", i.e. other languages equivalents of "kaboom" and the like.

A cartoon panel of an old Victorian (?) home with lots of forest and shrubbery in the background. In the sky above the house the words هاهاها، هاهاها hang in the air, transliterating hearty laughter that can be heard outside

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Philipp Wacker @phkwacker.bsky.social · 20/04/2025

Finally time for baking over the holidays. Rye/wheat

Two long-ish loaves of bread, dark brown color, with diagonal cuts

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Philipp Wacker @phkwacker.bsky.social · 24/03/2025

In fact, let's focus on this part: We should read this as something in the form f(C_1) - f(C_0) - Df(C_0)[C_1-C_0], where f(C) = ln(det(C)) (and C instead of Sigma). I believe this is also due to the connection of KL-divergence to Bregman divergences in general (en.wikipedia.org/wiki/Bregman...).

$Just the matrix-dependent quantities: \ln \det \Sigma _{1} - \ln \det \Sigma _{0} - \operatorname {tr} \left(I-\Sigma _{1}^{-1}\Sigma _{0}\right)$

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Philipp Wacker @phkwacker.bsky.social · 24/03/2025

This makes sense if we rewrite the expression a bit:

$A slight rewrite of the KL divergence, pulling apart the logarithmic determinants, and including the constant k as the trace of an identity matrix: {\displaystyle D_{\text{KL}}\left({\mathcal {N}}_{0}\parallel {\mathcal {N}}_{1}\right)={\frac {1}{2}}\left(\ln \det \Sigma _{1} - \ln \det \Sigma _{0} - \operatorname {tr} \left(I-\Sigma _{1}^{-1}\Sigma _{0}\right)+\left(\mu _{1}-\mu _{0}\right)^{\mathsf {T}}\Sigma _{1}^{-1}\left(\mu _{1}-\mu _{0}\right)\right).}$

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Philipp Wacker @phkwacker.bsky.social · 24/03/2025

Something cool I understood this week: The Kullback-Leibler divergence between two multivariate Gaussian distributions has a closed form solution. The term with the means somehow makes sense: Penalise a covariance-weighted squared distance between the respective means. But all these matrix terms?

$Formula for KL divergence between two Gaussians N_0 and N_1 {\displaystyle D_{\text{KL}}\left({\mathcal {N}}_{0}\parallel {\mathcal {N}}_{1}\right)={\frac {1}{2}}\left(\operatorname {tr} \left(\Sigma _{1}^{-1}\Sigma _{0}\right)-k+\left(\mu _{1}-\mu _{0}\right)^{\mathsf {T}}\Sigma _{1}^{-1}\left(\mu _{1}-\mu _{0}\right)+\ln \left({\frac {\det \Sigma _{1}}{\det \Sigma _{0}}}\right)\right).}$

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Philipp Wacker @phkwacker.bsky.social · 23/03/2025

Ah, very interesting! Look at this: This is the output of $Y_i Y_i^\top$ $Y_i {Y_i}^\top$ (note the brackets)

$PDF LaTeX output of $Y_i Y_i^\top$ $Y_i {Y_i}^\top$. First version has wrong alignment of i, second one is correct.$

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Philipp Wacker @phkwacker.bsky.social · 23/03/2025

What's happening with the indices here? Why are they not aligned?

$PDF LaTeX output of $Y_i Y_i^\top$. The heights of the two indices i are not aligned.$

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Philipp Wacker @phkwacker.bsky.social · 06/02/2025

I (think I) finally figured out a Venn diagram for all these pesky set systems: sigma algebra, lambda-system, algebra, monotone class, pi-system!

A Venn diagram of five properties: sigma-algebra, algebra, lambda -system, monotone class, and pi-system

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Philipp Wacker @phkwacker.bsky.social · 27/12/2024

Don't look back, you'll trip over Michael Caine!

Book cover. Title: dont look back, you'll trip over, by Michael Caine

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Philipp Wacker @phkwacker.bsky.social · 18/12/2024

I can't get over how these cats are drawn. Pure nightmare fuel

Children's book with two drawn cats. Cats look normal with the exception that their mouths are somehow in the middle of their belly.

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Philipp Wacker @phkwacker.bsky.social · 13/12/2024

Apparently, math conferences go like this: It's raining, everyone sits/stands in a puddle while some dude tries to convince everyone that pi=3.14, to the confusion of everyone, while notes taken dissolve in the puddle, letters and numbers floating away.

It's raining, 2 men and one woman sit in a puddle while some dude tries to convince everyone that pi=3.14, to the confusion of everyone, while notes taken dissolve in the puddle, letters and numbers floating away.

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Philipp Wacker @phkwacker.bsky.social · 18/11/2024

Summarising: The three different models have different bias-variance decompositions. The constant model has considerable bias (red point cloud not centered around ground truth), but it has low variance (small spread). Order 5 has minimal bias, but high variance. Quadratic seems good compromise.

Constant models: Considerable bias, low variance. Polynomial order 5: Low bias, high variance. Quadratic polynomial somewhere in the middle.

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Philipp Wacker @phkwacker.bsky.social · 18/11/2024

And this is for 1000 independent models of polynomials, order 5.

Ensemble of order-5 polynomial regression lines, showing a very wide spread of predictions around a ground truth (blue cross)

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Philipp Wacker @phkwacker.bsky.social · 18/11/2024

Here the same thing for 1000 independent "quadratic" models of type f(x) = b0 + b1*x+ b2*x^2.

Ensemble of quadratic regression lines, showing a spread of predictions as a red point cloud around a ground truth (blue cross)

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Philipp Wacker @phkwacker.bsky.social · 17/11/2024

Look at this neat visualisation of the bias-variance trade-off in statistical learning I made: We look at a fixed dataset (black dots) and do 1000 independent "constant" regressions of type f(x) = b_0 using random subsamples of the data. Red dots are predictions for a fixed point (blue cross)

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Philipp Wacker @phkwacker.bsky.social · 06/11/2024

Microsoft is getting scarily good at inferring my mental state and sending me subtle messages via AI-generated alt texts.

Screenshot of a graph inserted into Microsoft Powerpoint, with the AI-generated Alt Text "A graph of a person in a cave" (which is not what can be seen on the inserted graph at all, instead showing a corner plot with a bivariate distribution). This alt text was not generated by MS Powerpoint

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Philipp Wacker @phkwacker.bsky.social · 05/11/2024

Here's the data for "Treatment B", a competing method. On the patients in the small stones group, it had a success rate of 85%, in the large stones group, 65%. Clearly, Treatment A is better for both small and large kidney stones, right?

A graphical representation of the following statistics: 240 patients treated with "Treatment A" for kidney stones in total. 200 of them have small stones, with a recovery rate of 85% (with 170 patients recovered). The remaining 40 patients have large stones, with a recovery rate of 65% (26 recovered). In short: 85% of small stones patients recovered, 65% of large stones patients recovered.

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Philipp Wacker @phkwacker.bsky.social · 05/11/2024

To distract ourselves, some recreational Stats! Here's a fictional dataset for "Treatment A" on kidney stones. Each square is a patient, 1/3 of them have small kidney stones, 2/3 have large kidney stones. We can see that Treatment A has a success rate of 90% on small stones, and 70% on large stones.

A graphical representation of the following statistics: 240 patients treated with "Treatment A" for kidney stones in total. 80 of them have small stones, with a recovery rate of 90% (with 36 patients recovered). The remaining 160 patients have large stones, with a recovery rate of 70% (112 recovered). In short: 90% of small stones patients recovered, 70% of large stones patients recovered.

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